Re: Controversial
From: gellda@umich.edu (David A. Gell)
Date: 1996/02/06
MessageID: gellda-0602962221190001@sprl-mac131.sprl.umich.edu
references: <4f8aj1$j8j@newsbf02.news.aol.com>
organization: Space Physics Research Lab, University of Michigan
newsgroups: rec.models.rc.air
In article <4f8aj1$j8j@newsbf02.news.aol.com>, terrantula@aol.com
(Terrantula) wrote:
#I wanted a chance to jump back in here before this thread dies, so here
#goes.
#
#
#
#My problem was with the way scientists and engineers attempt to explain
#lift to the layman. When I said I never had any faith in the explaination
#given by Bernoulli's Principle, it wasn't Bernoulli I was challenging. I
#have a science degree and recognize a law of physics when somebody beats
#me over the head with it. What I was (and still am) troubled with was the
#standard way lift was explained for the past 30 years in aviation texts
#aimed at pilots as well as the general public.
#
#That explanation was that since the air traveling over the top of the wing
#had to meet up the air traveling under the wing at the same time (at the
#trailing edge), and since the distance traveled over the top of the wing
#was greater, the air moving over the top has to go faster to "catch up" to
#the air moving across the bottom of the wing. Bernoulli's principle was
#then thrown in to explain the reduced pressure created by the faster
#airflow. What this thread has done is demonstrate that we have an invalid
#cause/effect relationship. In other words, though we can use Bernoulli's
#principle to explain lift, the first part of the assumption is invalid and
#doesn't logically lead to the "effect".
#
#So here's the question. I'm still having a hard time visualizing what's
#going on. When it was pointed out that the air moving over the top of the
#wing actually reached the trailing edge BEFORE the air traveling across
#the bottom, it got even tougher for me to visualize. Is there anyone who
#can describe what's going on in a way that is possible to visualize
#without oversimplifying to the point of invalidity? If this is impossible,
#I guess I'll have to accept it. I just hate telling a student that his
#airplane flys do to a mystical phenomena that is impossible to explain.
#
#Terry Gamble (terrantula@aol.com)
#Phoenix, Arizona
I posted the following earlier in this thread, maybe you missed it, so
I'll try again. This posting should be read after reading the Model
Airplane News article by Raskin, since it refers to some figures in that
article.
I'm going to take a stab at relating pressure, Burnouli, under-cambered
wings...again.
The interaction of objects and forces are governed by Newton's laws of
motion. The three laws are:
1) An object at rest (or in uniform motion) remains at rest (or in
uniform motion) unless acted on by a force. In other words, it
doesn't move unless pushed.
2) The change in momentum is proportional to the applied force. This is
also stated as the acceleration of an object is proportional to
the applied force and inversely proportional to the object's mass.
In other words, push hard to change velocity rapidly.
3) If one object applies a force to another, the second object applies
an equal and opposite force to the first. This is also stated as every
action has an equal and opposite reaction. In other words if I push it,
it pushes me back.
Now, how are these rules applied to a wing in the air. The wing and the
air molecules are objects that interact with forces. The forces between
air molecules are called viscosity. One could, in principal, calculate
the force on each molecule due to every other molecule and due to the
presence of the wing, apply Newton's laws and determine the forces. In
reality, this is not practical, so Newton's laws are manipulated
mathematically to obtain other descriptions of the behavior of the air and
the wing. You can obtain expressions for the behavior of parcels of air,
the Momentum equation, the conservation of Mass and Burnouli's principal.
Now, why does a wing produce lift? Simply, the wing when immersed in a
flowing gas deflects the flow. The only way it can do that (1st law) is
to apply a force to the gas. The details of the force don't really matter
at this point, just the fact that there is a force. Since the wing
applies a force to the air, the air applies a force to the wing (3rd law).
If the wing is at higher angle of attack, it deflects the air more
strongly, thus it is applying a larger force to the air (2nd law) and the
lift is higher. If the wing deflects more air (flying at a higher
airspeed) the lift is also higher. The actual mechanism that causes the
deflection is the complicated interactions between the air molecules
(viscosity) and between the air molecules and the surface of the wing
(shear forces). It is not simply air molecules bouncing off of the wing
surface. One observed consequence of these interactions is the Kutta
condition, that states that there is a stagnation point at the trailing
edge of a body in a flowing gas.
Now, what about Burnouli?. Burnouli's principal is an expression of
conservation of energy. If properly applied, a calculation of the
pressure differences using this pricipal result in the exact same lift as
application of another set of equations. What is often missed in the
simple explainations of lift, using Burnouli's principal, is that there is
no requirement for the air flow over one surface of the wing to get to the
trailing edge at the same time as that flowing over the other surface.
So, for example, the contents of the side bar in the MAN artical by
Raskin entitled "The Numbers Just Don't Add Up" is not correct. The title
is correct, but the content isn't because the author assumes that the air
over the top gets to the trailing edge at the same time as that travelling
over the bottom. It doesn't, it gets there first. How much faster? Fast
enough so that the pressure differences obtained by using Burnouli's
principal exactly provide the observed lift.
Now, why does an undercambered wing produce lift? One might think, using
Burnoulis principal naively (as the MAN article did), that since the upper
and lower surfaces are the same length, AND (incorrect assumption alert)
the flow over each surface must get to the trailing edge at the same time,
the gas flow on the upper and lower surfaces are have the same speed, and
therefore there is no pressure difference. If, this were true, the wing
would not deflect the airflow at all, and there would be no lift. An
undercambered airfoil does in fact deflect the airflow, and therefore,
using Newton's First Law, must have applied a force to the air.
One way of thinking about airfoils, is to consider them as a camber line
wrapped in a fairing. The camber line is the line of points midway
between the upper surface and the lower surface of the wing. It is not
the same, in general, as the chord line which is a straight line between
the leading and trailing edges of the wing. The shape of the camber line
affects properties of the airfoil such as the zero-lift angle of attack,
the zero lift pitching moment, and maybe others that I've forgotten. The
shape of the fairing affects other properties, such as the zero lift
drag. In the case of a symetrical wing, the chord and camber lines are
the same, the wing produces zero lift at zero angle of attack. For a
symetrical wing to produce lift, it must be at an angle of attack. A flat
bottom wing, such as used on many trainers, has a curved camber line. You
can imagine the camber line as one of the streamlines of the flow over the
wing. Since it is curved, the airflow is deflected by the wing, even when
the wing is at zero angle of attack. To obtain zero lift, the wing must
be flown at a slight negative angle of attack. Thus, inverted flight with
such a wing requires lots of down elevator to hold the wing at the
appropriate negative angle of attack.
When you thing of wings in this manner, the examples shown in figures 2
through 6 are much easier to understand. Figure 2, the undercambered
wing, has a curved camber, and deflects the air. Figure 3, the WWI
airfoil (also bird wing), has curved camber, deflects air correctly, and
produces lift. Figure 4, the humpty bump airfoil, has a camber line that
alternately directs the airflow downward, then upward resulting in no net
downward deflection of the air and no lift.
--
David A. Gell |
University of Michigan |
Space Physics Research Lab |